ABCD IS TRAPEZIUM IN WHICH AB IS PARALELL TO CD AND AD=BC.SHOW THAT

ANGLE A =ANGLE B

ANGLE C=ANGLE D

 Hi!

Given- a trapezium with AB ll DC and AD=BC

Construction- Join AC and BD

To prove- angle A=angle B

                  angle D=angle C

Proof-     In triangle ABD and CBD

                angleADB=angleCBD    (alternate interior angles of 2 triangles)

               angle ABD=angleCDB   (alternate interior angles of 2 triangles)

                BD=BD                             (common side)

Therefore, triangleABD =~ triangle CBD

By CPCT-angle A= angle C         .....................eq-1

Similarly,

triangle ACD=~ triangle ACB

By CPCT angle D=angle B              .......................eq-2

By equation 1 and 2 we obtain

angle A=B=C=D

hence_ proved

Sorry for figure

hope this helps.